Now that Twitter has removed the "via" information from their web interface, here's the only way I could think of to find it again... Of course, if you're the kind of person who cares about the originating client, you'll be using a 3rd party client. Twitter's Tweetdeck still displays the source.

1. Get tweet source data
Open the tweet, click Details
Expand the tweet, click Details
Get tweet source data Page 1

2. Get tweet source data
Unique Tweet
Grab the unique tweet ID
Get tweet source data Page 2

3. Get tweet source data
In theory...
Go to:
https://api.twitter.com/1/statuses/show.json?id=TWEETID
Search for "source"
(be very careful to use version 1 of the API.)
Get tweet source data Page 3